Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoA
The monogamy property of entanglement is an intriguing feature of multipartite quantum entanglement. Most entanglement measures satisfying the monogamy inequality have turned out to be convex. Whether nonconvex entanglement measures obey the monogamy inequalities remains less known at present. As a...
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| Формат: | Стаття |
| Мова: | English |
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MDPI AG
2024-01-01
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| Серія: | Entropy |
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| Онлайн доступ: | https://www.mdpi.com/1099-4300/26/2/127 |
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| author | Zhongxi Shen Dongping Xuan Wen Zhou Zhixi Wang Shao-Ming Fei |
| author_facet | Zhongxi Shen Dongping Xuan Wen Zhou Zhixi Wang Shao-Ming Fei |
| author_sort | Zhongxi Shen |
| collection | DOAJ |
| description | The monogamy property of entanglement is an intriguing feature of multipartite quantum entanglement. Most entanglement measures satisfying the monogamy inequality have turned out to be convex. Whether nonconvex entanglement measures obey the monogamy inequalities remains less known at present. As a well-known measure of entanglement, the logarithmic negativity is not convex. We elucidate the constraints of multi-qubit entanglement based on the logarithmic convex-roof extended negativity (LCREN) and the logarithmic convex-roof extended negativity of assistance (LCRENoA). Using the Hamming weight derived from the binary vector associated with the distribution of subsystems, we establish monogamy inequalities for multi-qubit entanglement in terms of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>th-power (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>≥</mo><mn>4</mn><mo form="prefix">ln</mo><mn>2</mn></mrow></semantics></math></inline-formula>) of LCREN, and polygamy inequalities utilizing the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>th-power (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo>≤</mo><mi>α</mi><mo>≤</mo><mn>2</mn></mrow></semantics></math></inline-formula>) of LCRENoA. We demonstrate that these inequalities give rise to tighter constraints than the existing ones. Furthermore, our monogamy inequalities are shown to remain valid for the high-dimensional states that violate the CKW monogamy inequality. Detailed examples are presented to illustrate the effectiveness of our results in characterizing the multipartite entanglement distributions. |
| first_indexed | 2024-03-07T22:33:55Z |
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| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-07T22:33:55Z |
| publishDate | 2024-01-01 |
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| series | Entropy |
| spelling | doaj.art-bbbf0525003c427f93b80cfff9a67fd82024-02-23T15:15:40ZengMDPI AGEntropy1099-43002024-01-0126212710.3390/e26020127Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoAZhongxi Shen0Dongping Xuan1Wen Zhou2Zhixi Wang3Shao-Ming Fei4School of Mathematical Sciences, Capital Normal University, Beijing 100048, ChinaSchool of Mathematical Sciences, Capital Normal University, Beijing 100048, ChinaSchool of Mathematical Sciences, Capital Normal University, Beijing 100048, ChinaSchool of Mathematical Sciences, Capital Normal University, Beijing 100048, ChinaSchool of Mathematical Sciences, Capital Normal University, Beijing 100048, ChinaThe monogamy property of entanglement is an intriguing feature of multipartite quantum entanglement. Most entanglement measures satisfying the monogamy inequality have turned out to be convex. Whether nonconvex entanglement measures obey the monogamy inequalities remains less known at present. As a well-known measure of entanglement, the logarithmic negativity is not convex. We elucidate the constraints of multi-qubit entanglement based on the logarithmic convex-roof extended negativity (LCREN) and the logarithmic convex-roof extended negativity of assistance (LCRENoA). Using the Hamming weight derived from the binary vector associated with the distribution of subsystems, we establish monogamy inequalities for multi-qubit entanglement in terms of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>th-power (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>≥</mo><mn>4</mn><mo form="prefix">ln</mo><mn>2</mn></mrow></semantics></math></inline-formula>) of LCREN, and polygamy inequalities utilizing the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>th-power (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo>≤</mo><mi>α</mi><mo>≤</mo><mn>2</mn></mrow></semantics></math></inline-formula>) of LCRENoA. We demonstrate that these inequalities give rise to tighter constraints than the existing ones. Furthermore, our monogamy inequalities are shown to remain valid for the high-dimensional states that violate the CKW monogamy inequality. Detailed examples are presented to illustrate the effectiveness of our results in characterizing the multipartite entanglement distributions.https://www.mdpi.com/1099-4300/26/2/127monogamypolygamyLCRENLCRENoA |
| spellingShingle | Zhongxi Shen Dongping Xuan Wen Zhou Zhixi Wang Shao-Ming Fei Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoA Entropy monogamy polygamy LCREN LCRENoA |
| title | Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoA |
| title_full | Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoA |
| title_fullStr | Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoA |
| title_full_unstemmed | Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoA |
| title_short | Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoA |
| title_sort | tighter constraints of multi qubit entanglement in terms of nonconvex entanglement measures lcren and lcrenoa |
| topic | monogamy polygamy LCREN LCRENoA |
| url | https://www.mdpi.com/1099-4300/26/2/127 |
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